The National Labor Relations Board has proposed rolling back an Obama-era job ruling that made it easier for contractors and workers at franchised businesses to form unions and collectively bargain with big corporations.

On Thursday, the body overseeing union-employer disputes released a proposal to abandon a 2015 decision by the prior, Democratic-controlled board that ruled a company could be held liable if it illegally interfered with workers’ rights to organize a union, even if those employees didn’t directly work for the...